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Collapse Postulates

What about treating the collapse as the Bayesian probabilities update in light of the measurement (new evidence)?

There are lots of thought experiments and actual experiments that suggest this view doesn't work. "PBR" is the one that springs to mind. Some people still support this view, but I've never seen any of them straightforwardly state what they think the underly reallity (that the amplitudes are supposed to represent beliefs about) actually is.
I think Bell's theorem rules out exactly this reading. Unless you just redefine probability to include all the math of QM, but I feel inclined to call that a vile heresy.